Suppose that you want to build a transformer that will convert 70 V power coming in the primary coil to 245 V power going out of the secondary coil. What is the smallest total number of turns (primary turns plus secondary turns) you need to create the transformer?
A) 63
B) 9
C) 7
D) 315
B) 9
The ratio of the primary voltage to the secondary voltage is 70V:245V, which simplifies to 2:7. This means the ratio of the number of turns in the primary coil to the number of turns in the secondary coil should also be 2:7.
Let's call the number of turns in the primary coil "x" and the number of turns in the secondary coil "7x".
Therefore, the total number of turns needed would be x + 7x = 8x.
To find the smallest total number of turns, we'll try different values for x:
If x = 1, then the total number of turns = 8
If x = 2, then the total number of turns = 16
If x = 3, then the total number of turns = 24
If x = 4, then the total number of turns = 32
If x = 5, then the total number of turns = 40
If x = 6, then the total number of turns = 48
If x = 7, then the total number of turns = 56
If x = 8, then the total number of turns = 64
If x = 9, then the total number of turns = 72
Therefore, the smallest total number of turns to create the transformer is 9.